1. Field of the Invention
The invention described herein is related to non-parametric spectral analysis of discrete time data. More specifically, the invention implements a spectrum analyzer using a polyphase filter bank derived from a high order prototype filter. The order of the prototype filter may be chosen so as to cede time resolution in favor of improved frequency resolution.
2. Description of the Prior Art
For many applications in which non-stationary signals are typically encountered, such as in sonar (an acronym for sound navigation and ranging), short-time spectral analysis is often used, i.e., analysis performed over relatively brief segments during which spectral properties are assumed stable. In sonar, as in other applications like general audio, when analytical models of the data are not well-understood, non-parametric analysis is utilized. Ubiquitous in non-parametric analysis is the Discrete Fourier Transformer (DFT), which is implemented efficiently by the Fast Fourier Transform. This efficiency has helped DFT-based techniques dominate sonar spectral analysis. Indeed, DFT-based approaches are, of course, also widely utilized in many other spectral analysis applications.
Filter banks can also serve as effective spectrum analyzers. The filter bank spectrum analyzer is most commonly discussed for constant sample rate, stationary spectral analysis, where each output of a bank of M complex, uniform, bandpass filters is integrated over time. However, the M outputs at each sample can also be considered estimates of the short-time spectrum, and thus filter banks can provide a non-stationary analyzer as required for sonar or audio signals.
Although DFT-based spectral analysis is most often viewed as a block processing operation, it is well-known that the DFT can also be mapped into a sample-by-sample, or stream-oriented filter bank framework. The filter bank structure falls under the general class of subband coding, i.e., a transformation of a time-domain sequence into frequency-domain subbands, where subsequent processing can be performed on each band output. Subband filter structures now dominate audio and image analysis-synthesis systems for four main reasons: (1) they can remove redundancy in the frequency domain by exploiting spectral structure; (2) sophisticated psychophysical models incorporated in the frequency domain can aid in quantization and bit allocation; (3) the structures can be very efficiently implemented with multirate techniques; and, (4) any aliasing caused by multirate techniques can be almost entirely eliminated when used in analysis-synthesis tandems.
Despite its popularity in coding applications, multirate subband structures have not been considered for use as general purpose spectrum analyzers. This is due in part to the fact that, in spectral analysis, filters should permit little aliasing, while audio coders are often designed to allow considerable aliasing, as in the M-channel, maximally-decimated, quadrature mirror filter bank, popular in audio encoding. In subsequent audio decoding, the aliasing is exactly eliminated in a process called perfect reconstruction.
However, in spectral analysis, unlike in coding, no decoding is performed so aliasing cannot be eliminated. Because multirate subband structures have rarely been considered outside the context of perfect reconstruction coding, failure to cancel aliasing has been the primary obstacle in such structures being utilized in general purpose spectral analysis. Furthermore, the redundancy removal and psychophysical advantages mentioned for coding systems are not relevant to stand-alone spectrum analyzers. Thus, as most of the advantages mentioned previously no longer hold, the utility of multirate subband structures as stand-alone spectrum analyzers has not been widely recognized. An exception to this is the work of Tkacenko and Vaidyanathan in the Journal Paper, Sinusoidal Frequency Estimation Using Filter Banks (Proceedings of ICASSP, Vol. 5, 2001, pp. 3089–3092), where a multirate filter bank spectrum analyzer was used to estimate the frequency of a stationary sinusoid in noise. However, the spectrum analyzer of Tkacenko and Vaidyanathan utilizes a staionary, parametric model and, thus, its use in general purpose spectral analysis is extremely limited.
U.S. Pat. No. 6,085,077 to Fields, et al., discloses a digital channelized receiver using a uniform filter bank of polyphase bandpass filters. The disclosed receiver is adapted to acquire an instantaneous frequency measurement through assigning a predetermined relationship between each filter's frequency response, the decimation rate of the data on each filter channel, and the number of filters in the receiver. However, as the design of the disclosed filter bank is set by goals of hardware efficiency, effects of aliasing on the signal are overlooked. The effects of aliasing decreases the signal-to-noise ratio, which is especially problematic near the passband edges, as disclosed in the Specification of the reference. In obtaining an instantaneous frequency measurement, the disclosed invention requires additional circuitry at the output of the filter bank.
The mitigation of aliasing has been addressed by the inventors of the present invention and is discussed in their journal paper, “Multirate Spectral Analysis for Passive Sonar”, (Integrated Computer-Aided Engineering, Vol. 10, No. 1, 2003, pp. 91–108). The inventors found that increasing the order of the prototype filter used to obtain the polyphase components by a significant degree so as to approach an ideal low-pass filter greatly overcomes aliasing caused by decimation. In so doing, however, a sacrifice in temporal localization must be tolerated. Thus, relief from aliasing in this manner may not be acceptable in certain applications, including that described in U.S. Pat. No. 6,085,077, which requires an instantaneous measurement. Thus, the system disclosed by the above-referenced U.S. patent requires additional system components to obtain the instantaneous frequency measurement through the aliasing.
One of the shortcomings of filter bank spectral analyzers of the prior art, including the system disclosed by the above-referenced U.S. patent and the present inventor's own work, is that the temporal overlap used in the spectral estimation is confined to integer values equal to the ratio of the number of filters to the decimation factor on each channel. In many applications, this limitation reduces the ability for system optimization by, for example, requiring additional time to obtain spectra that may have more overlap than required or decreasing the accuracy in the spectral estimate by not having enough overlap in the temporal data stream.
In view of the shortcomings of the prior art, there is an apparent need for a general purpose spectral analysis tool having a greater degree of freedom in the selection of overlap in the temporal data for spectral estimation that affords, where allowable, a trade-off in temporal resolution in favor of improved spectral resolution.